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The basic approach to all piping systems is to write the Bernoulli equation between two points, connected by a streamline, where the conditions are known. For example, between the surface of a reservoir and a pipe outlet.

The total head at point 0 must match with the total head at point 1, adjusted for any increase in head due to pumps, losses due to pipe friction and so-called "minor losses" due to entries, exits, fittings, etc. Pump head developed is generally a function of the flow through the system

Friction losses are a complex function of the system geometry, the fluid properties and the flow rate in the system. By observation, the head loss is roughly proportional to the square of the flow rate in most engineering flows (fully developed, turbulent pipe flow). This observation leads to the Darcy-Weisbach equation for head loss due to friction

Reynolds Number is the fundamental dimensionless group in viscous flow. Velocity times Length Scale divided by Kinematic Viscosity. Relative Roughness relates the height of a typical roughness element to the scale of the flow, represented by the pipe diameter, D. Pipe Cross-section is important, as deviations from circular cross-section will cause secondary flows that increase the pressure drop. Non-circular pipes and ducts are generally treated by using the hydraulic diameter, in place of the diameter and treating the pipe as if it were round

For turbulent flow, Colebrook (1939) found an implicit correlation for the friction factor in round pipes. This correlation converges well in few iterations. Convergence can be optimized by slight under-relaxation.

From Q and piping determine Reynolds Number, relative roughness and thus the friction factor. Substitute into the Darcy-Weisbach equation to obtain head loss for the given flow. Substitute into the Bernoulli equation to find the necessary elevation or pump head

Obtain the allowable head loss from the Bernoulli equation, then start by guessing a friction factor. (0.02 is a good guess if you have nothing better.) Calculate the velocity from the Darcy-Weisbach equation. From this velocity and the piping characteristics, calculate Reynolds Number, relative roughness and thus friction factor.

Repeat the calculation with the new friction factor until sufficient convergence is obtained. Q = VA

Although they often account for a major portion of the head loss, especially in process piping, the additional losses due to entries and exits, fittings and valves are traditionally referred to as minor losses. These losses represent additional energy dissipation in the flow, usually caused by secondary flows induced by curvature or recirculation. The minor losses are any head loss present in addition to the head loss for the same length of straight pipe.

Like pipe friction, these losses are roughly proportional to the square of the flow rate. Defining K, the loss coefficient, by